Design Method of Control System, Control Method, Storage Medium Storing Computer Program, and Control Apparatus

1. A design method of a control system including a feedback controller that calculates a control input u to a controlled object, the feedback controller following a transfer function C(ρ), the control system being configured to control the controlled object by calculating the control input u based on a desired value r and on a control output y from the controlled object, the design method comprising: acquiring time-series data of a set of a sample um of the control input u and a sample ym of the control output y; calculating, based on the time-series data, a value ρ* of a parameter ρ that minimizes a value of an evaluation function J(ρ,θ,um,ym) in a state where a parameter θ in the evaluation function J(ρ,θ,um,ym) is set to an initial value θini corresponding to a target response yr, the evaluation function J(ρ,θ,um,ym) including a target response transfer function Td(θ) and the transfer function C(ρ) as elements, the target response transfer function Td(θ) defining a target response yr=Td(θini)r that is a target value of the control output y relative to the desired value r, the evaluation function J(ρ,θ,um,ym) being for evaluating an error between the target response yr and the control output y from the sample um and the sample ym; calculating, based on the time-series data, a value θ* of a parameter θ that minimizes the value of the evaluation function J(ρ,θ,um,ym) in a state where the parameter ρ in the evaluation function J(ρ,θ,um,ym) is set to the value ρ*; and designing the control system based on the initial value Gini and the calculated value θ* and ρ*, the control system including a feedforward controller and the feedback controller, the feedforward controller being configured to receive input of the desired value r and to calculate a value r*=G(θini,θ*)r following a transfer function G(θini,θ*), the feedback controller being configured to calculate a control input u=C(ρ*)(r*−y) following a transfer function C(ρ=ρ*) based on a deviation r*−y between the value r* and the control output y, the value r* being calculated by the feedforward controller, the transfer function G(θini,θ*) being a transfer function Td(θini)/Td(θ*).

3. The design method according to claim 1 , wherein the designing the control system includes: in response to determining that a difference between a predicted response yr*=Td(θ*)r and the target response yr=Td(θini)r is larger than or equal to a standard, designing a control system including the feedforward controller and the feedback controller; and in response to determining that the difference is smaller than the standard, designing a control system without the feedforward controller, the control system including a feedback controller configured to calculate a control input u=C(ρ*)(r−y) following the transfer function C(ρ*) based on a deviation r−y between the desired value r and the control output y.

4. A control method in a control system including a feedback controller that calculates a control input u to a controlled object, the feedback controller following a transfer function C(ρ), the control system being configured to control the controlled object by calculating the control input u based on a desired value r and on a control output y from the controlled object, the control method comprising: acquiring time-series data of a set of a sample um of the control input u and a sample ym of the control output y; calculating, based on the time-series data, a value ρ* of a parameter ρ that minimizes a value of an evaluation function J(ρ,θ,um,ym) in a state where a parameter θ in the evaluation function J(ρ,θ,um,ym) is set to an initial value θini corresponding to a target response yr, the evaluation function J(ρ,θ,um,ym) including a target response transfer function Td(θ) and the transfer function C(ρ) as elements, the target response transfer function Td(θ) defining a target response yr=Td(θini)r that is a target value of the control output y relative to the desired value r, the evaluation function J(ρ,θ,um,ym) being for evaluating an error between the target response yr and the control output y from the sample um and the sample ym; calculating, based on the time-series data, a value θ* of a parameter θ that minimizes the value of the evaluation function J(ρ,θ,um,ym) in a state where the parameter ρ in the evaluation function J(ρ,θ,um,ym) is set to the value ρ*; designing the control system based on the initial value θini and the calculated value θ* and ρ*, the control system including a feedforward controller and the feedback controller, the feedforward controller being configured to receive input of the desired value r and to calculate a value r*=G(θini,θ*)r following a transfer function G(θini,θ*), the feedback controller being configured to calculate a control input u=C(ρ*)(r*−y) following a transfer function C(ρ=ρ*) based on a deviation r*−y between the value r* and the control output y, the value r* being calculated by the feedforward controller, the transfer function G(θini,θ*) being a transfer function Td(θini)/Td(θ*), and controlling the controlled object based on the designed control system.

5. The control method according to claim 4 , further comprising: updating the designed control system by updating the value θ* of the transfer function G(θini,θ*) of the feedforward controller based on observation values of the control output y during a period in which the controlled object is controlled and on the value r* calculated by the feedforward controller during the period.

6. The control method according to claim 5 , wherein the updating the designed control system includes: calculating, based on the observation values of the control output y during the period and on the value r*, a value θn of the parameter θ that minimizes a value of an evaluation function K1(θ) or an evaluation function K2(θ) including the target response transfer function Td(θ) shown below K ⁢ 1 ⁢ ( θ ) =  y - T d ⁡ ( θ ) ⁢ r *  2 K ⁢ 2 ⁢ ( θ ) =  T d ⁡ ( θ i ⁢ n ⁢ i ) ⁢ r * - T d ⁡ ( θ i ⁢ n ⁢ i ) T d ⁡ ( θ ) ⁢ y  2 ; and updating the value θ* of the feedforward controller based on the calculated value θn.

7. The control method according to claim 6 , wherein the updating the control system is executed repeatedly; and wherein the updating the value θ* of the feedforward controller includes updating the value θ* of the feedforward controller with a moving average of the calculated value θn.

8. The control method according to claim 6 , wherein the updating the control system is executed repeatedly; and wherein the updating the value θ* of the feedforward controller includes updating the value θ* of the feedforward controller with a value obtained by removing a high-frequency component from the calculated value θn by using a low-pass filter.

9. The control method according to claim 5 , wherein the updating the designed control system includes: calculating the value θn based on the observation value of the control output y and on the value r* during a period in which a control is stable; and correcting the value θ* of the feedforward controller based on the calculated value θn, thereby updating the designed control system.

10. The control method according to claim 4 , wherein the control system is a motor drive system provided in a printer, the motor drive system including a motor and being configured to control a reciprocating motion of a carriage on which a recording head is mounted, the control input u being a current command value or a voltage command value to be inputted to the motor, the control output y being a position, a velocity, or an acceleration of the carriage which is the controlled object.

11. The control method according to claim 4 , wherein the control system is a motor drive system provided in a printer, the motor drive system including a motor and being configured to control a rotation motion of a roller that conveys paper in a paper conveyance mechanism, the control input u being a current command value or a voltage command value to be inputted to the motor, the control output y being a rotational position, a rotational velocity, or a rotational acceleration of the roller or the motor which is the controlled object.

12. A non-transitory computer-readable storage medium storing a set of program instructions for a computer to execute processing of designing a control system including a feedback controller that calculates a control input u to a controlled object, the feedback controller following a transfer function C(ρ), the control system being configured to control the controlled object by calculating the control input u based on a desired value r and on a control output y from the controlled object, the set of program instructions, when executed by the computer, causing the computer to perform: acquiring time-series data of a set of a sample um of the control input u and a sample ym of the control output y; calculating, based on the time-series data, a value ρ* of a parameter ρ that minimizes a value of an evaluation function J(ρ,θ,um,ym) in a state where a parameter θ in the evaluation function J(ρ,θ,um,ym) is set to an initial value θini corresponding to a target response yr, the evaluation function J(ρ,θ,um,ym) including a target response transfer function Td(θ) and the transfer function C(ρ) as elements, the target response transfer function Td(θ) defining a target response yr=Td(θini)r that is a target value of the control output y relative to the desired value r, the evaluation function J(ρ,θ,um,ym) being for evaluating an error between the target response yr and the control output y from the sample um and the sample ym; calculating, based on the time-series data, a value θ* of a parameter θ that minimizes the value of the evaluation function J(ρ,θ,um,ym) in a state where the parameter ρ in the evaluation function J(ρ,θ,um,ym) is set to the value ρ*; and designing the control system based on the initial value θini and the calculated value θ* and ρ*, the control system including a feedforward controller and the feedback controller, the feedforward controller being configured to receive input of the desired value r and to calculate a value r*=G(θini,θ*)r following a transfer function G(θini,θ*), the feedback controller being configured to calculate a control input u=C(ρ*)(r*−y) following a transfer function C(ρ=ρ*) based on a deviation r*−y between the value r* and the control output y, the value r* being calculated by the feedforward controller, the transfer function G(θini,θ*) being a transfer function Td(θini)/Td(θ*).

13. The non-transitory computer-readable storage medium according to claim 12 , wherein the set of program instructions, when executed by the computer, causes the computer to further perform: updating the designed control system by correcting the value θ* of the transfer function G(θini,θ*) of the feedforward controller in the control system based on observation values of the control output y during a period in which the controlled object is controlled by the designed control system and on the value r* calculated by the feedforward controller during the period.

14. A control apparatus comprising: a motor; a driven object configured to be driven by the motor; a motor controller including a feedback controller that calculates a control input u to the motor, the feedback controller following a transfer function C(ρ), the motor controller being configured to control the motor and the driven object by calculating the control input u based on a desired value r and on a control output y from the driven object; and a main controller configured to: acquire time-series data of a set of a sample um of the control input u and a sample ym of the control output y; calculate based on the time-series data, a value ρ* of a parameter ρ that minimizes a value of an evaluation function J(ρ,θ,um,ym) in a state where a parameter θ in the evaluation function J(ρ,θ,um,ym) is set to an initial value θini corresponding to a target response yr, the evaluation function J(ρ,θ,um,ym) including a target response transfer function Td(θ) and the transfer function C(ρ) as elements, the target response transfer function Td(θ) defining a target response yr=Td(θini)r that is a target value of the control output y relative to the desired value r, the evaluation function J(ρ,θ,um,ym) being for evaluating an error between the target response yr and the control output y from the sample um and the sample ym; calculate, based on the time-series data, a value θ* of a parameter θ that minimizes the value of the evaluation function J(ρ,θ,um,ym) in a state where the parameter ρ in the evaluation function J(ρ,θ,um,ym) is set to the value ρ*; design the motor controller based on the initial value θini and the calculated value θ* and ρ*, the motor controller further including a feedforward controller, the feedforward controller being configured to receive input of the desired value r and to calculate a value r*=G(θini,θ*)r following a transfer function G(θini,θ*), the feedback controller being configured to calculate a control input u=C(ρ*)(r*−y) following a transfer function C(ρ=ρ*) based on a deviation r*−y between the value r* and the control output y, the value r* being calculated by the feedforward controller, the transfer function G(θini,θ*) being a transfer function Td(θini)/Td(θ*); and control the motor and the driven object based on the designed motor controller.